2 Answers
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Something is very very wrong with newer X11 and 82845G video hardware. I've actually downgraded to Slackware 11.0 on one machine to get reliable 82845G graphics.

My development machine runs Arch. The Arch forums have a 7-page multi-year thread about 82845G. If you look at about page 5 of the Arch forum thread, you can see that some people claim a fix. Arch provides 2 separate packages to deal with this issue. I haven't ever even installed Fedora, so I'm not sure what to recommend you try. I may try to install one of Arch's new packages, now that I'm aware of it.

I have seen this sort of problem caused by a bad motherboard. In my case when booting Fedora19 everything worked ok until the system started to render the graphics for the KDE gui. It then hung with an error message about failure of the render ring, mouse still worked and I could enter text mode, The system had worked previously and nothing was changed.

My mother board was about 10 years old and after exhausting other possibilities I took a close look at the board and found that a lot of the electrolytic capacitors (the aluminum cans with plastic sleeves) had failed. These capacitors filter spikes, caused by the logic switching, from the power supply lines and you can usually loose a few and never notice, but when enough fail the spikes get big enough to couple back into the logic. Since the logic switches into high gear when rendering that is when you first see the effect.

The capacitors fail because the liquid electrolyte in them slowly evaporates and when it gets low enough the capacitor shorts, heats the remaining electrolyte until it boils and ruptures the can and then briefly escapes as a jet of steam. The caps usually burn open so the computer keeps working. To check for this examine the caps with an X stamped in the top, that X is there to weaken the can so it will rupture without a catastrophic explosion. If the cap failed in this way the top will be slightly domed instead of flat, you may be able to see a tiny hole where the steam escaped and there may be a little brown or white residue near the hole.

This raises the question of replacing the caps. I tried that once on another board and it still didn't work. You can never be sure you got then all and doing that much unsoldering results in a high probability of damaging the board.